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Harry had never even imagined such a strange and splendid place. It was lit by thousands and thousands of candles that were floating in midair over four long tables, where the rest of the students were sitting. These tables were laid with glittering golden plates and goblets. At the top of the hall was another long table where the teachers were sitting. Professor McGonagall led the first years up here, so that they came to a halt in a line facing the other students, with the teachers behind them. The hundreds of faces staring at them looked like pale lanterns in the flickering candlelight. Dotted here and there among the students, the ghosts shone misty silver. Mainly to avoid all the staring eyes, Harry looked upward and saw a velvety black ceiling dotted with stars. He heard Hermione whisper, "Its bewitched to look like the sky outside. I read about it in Hogwarts: A History."

It was hard to believe there was a ceiling there at all, and that the Great Hall didn't simply open on to the heavens. (Harry Potter and the Sorcerer's Stone)

The phrase, at all, is not clear which meaning does it intensify: (1) hard to believe or (2) there was a ceiling there. Which one is it?

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    Note that at all is a negative polarity item (NPI) and can only occur in non-affirmative contexts, such as negative or interrogative constructions. But here, we find neither a question nor an explicit negative. Instead, we find hard to believe, which I think is an example of what Huddleston and Pullum call a "covertly negative lexical item", in this case expressing doubt. Its presence makes the clausal complement there was a ceiling there at all non-affirmative, so NPIs such as at all can appear. – snailboat Nov 21 '13 at 0:03
  • @snailboat, thank you. I've read it on page 835~6, after your commenent. – Listenever Nov 21 '13 at 0:21
  • @snailboat, NPIs, including 'at all', are on page 823. – Listenever Nov 21 '13 at 0:26
  • @snailboat This is ineresting because even if we consider something like: "I am surprised he can play violin at all, let alone so well", it is actually negative in some way since it is not flattering to the player, and I can see how this may be imagined to be a "non-affirmative context". Or, let's drag out something blunt like: "He seems so hopelessly incapable that I have trouble imagining how he can function at all". – Kaz Nov 21 '13 at 5:50
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    @Kaz In case you're interested, H&P further suggest that covert negatives fit into six semantic categories: 1. failure, avoidance, and omission; 2. prevention and prohibition; 3. denial; 4. doubt; 5. counter-expectation; and 6. unfavorable evaluation. – snailboat Nov 21 '13 at 5:56
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It's the second one. You can parse the sentence like this:

It was hard to believe (there was a ceiling there at all).

Where the thing that is hard to believe is the complete phrase "{that} there was a ceiling there at all".

At all simply emphasizes the lack of ceiling. The sentence would have the same meaning without it; this simply reinforces the statement. A few similar examples:

The room was so dirty that I'd be surprised if it had ever been cleaned (at all)!

The preacher works so hard to help others, but he is very poor. He hardly has anything (at all).

Billy behaved badly, so he was sent to bed without anything (at all) to eat.

All of these sentences would have the same meaning without at all; it only serves to reinforce what's being said (lack of cleanliness, lack of worldly possessions, lack of food; and in your example, lack of ceiling.)

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